1. Science & Technology Review
Nucleon Resonances
Bernhard A. Mecking
Jefferson Lab
Science & Technology Review
July 15, 2002
Introduction
Missing resonances
N D transition
Summary
My talk will be about the electroexcitation of nucleon resonances.
This conferences is all about nucleons and baryons.
Nathan Isgur has been a strong supporter of a nucleon research program at this laboratory. He formulated the importance of studies of the nucleon in 3 remarks he made at the N*2000 conferences in this auditorium:

2. Physics Goals Understand QCD in the strong coupling regime
example: bound qqq systems
mass spectrum, quantum numbers of nucleon excited states
what are the relevant degrees-of-freedom
wave function and interaction of the constituents
Source of information
dominated by pion-induced reactions (mostly pN pN)
advantage:
strong coupling large cross sections
simple spin structure
good quality beams
disadvantage: no structure information p p N* N N
insensitive to states with weak pN coupling

3. Theoretical Models Constituent quark model
3 constituent quarks
all 3 contribute to number of states
non-relativistic treatment (typically)
Refinements of the constituent quark model
restore relativity
hadronic form factors
coupling between decay channels
Lattice gauge calculations

4. Program Requirements Experiment Analysis
large high-quality data set for N* excitation covering
- a broad kinematical range in Q2, W, decay angles
- multiple decay modes (p, pp, h, r, w, K)
- polarization information (sensitive to interference terms)
Analysis
D(1232): full Partial Wave Analysis possible
(isolated resonance, Watson theorem)
higher resonances
- need to incorporate Born terms, unitarity, channel coupling
- full PWA presently not possible due to lack of data (polarization)
(substitute by assuming energy dependence of resonance)
- skills required at the boundary between experiment and theory

5. Quark Model Classification of N*
“missing” P13(1850) Capstick& Roberts
The SU(6)xO(3) symmetry scheme is a representation of the states in the symmetric constituent quark model, with L being the orbital angular momentum of the 3-quark system and energy levels in the harmonic oscillator potential. The states appear in supermultipets clustered in h-bar omega and orbital angular momentum.
The states are split in masses according to different quark-spin combinations. Empty boxes indicate predicted but unobserved or very uncertain states.
These arrows indicate the states I will be discussing in the following.

6. “Missing” Resonances?
Problem: symmetric CQM predicts many more states than have
been observed (in pN scattering)
Two possible solutions:
1. di-quark model
|q2q>
fewer degrees-of-freedom
open question: mechanism for q2 formation?
2. not all states have been found
possible reason: decouple from pN-channel
In recent years a number of alternatives to the "standard" constituent quark model have been proposed, in large measures to fix some of the real or perceived shortcomings of that model, especially to explain the absence of many states predicted in that model. Several talks at this conference are dedicated to these new approaches. One of the oldest alternative models is the quark-diquark model, where two of the quarks form an elementary object. This model has the advantage that due to the fewer excitation degrees of freedom a much smaller number of states are predicted which corresponds more to what we see in the data...
The various alternatives correspond to quite different underlying quark symmetries and interactions, search for at least some of the states predicted in the standard model, but not in the alternative models is imperative.
A series of P13 states with coupling to the omega channel are predicted in the standard model but not in the quark-diquark model
Electromagnetic production of omegas suffers from strong diffractive or t-channel contributions, leading to strong forward peaking which complicates the analysis. However, diffractive production is reduced with increasing Q2.
While the diffractive or t-channel contribution gives the forward peaking, s-channel resonance production produces a more symmetric angular dependence with significant large angle production.
(next) The data exhibit ..
|q3>
model calculations: missing states couple to
Npp (Dp, Nr), Nw, KY
g coupling not suppressed electromagnetic excitation is ideal

7. Electromagnetic Probe
helicity amplitudes very sensitive to the difference in wave functions of N and N*
can separate electric and magnetic parts of the transition amplitude
varying Q2 allows to change the spatial resolution and enhances different multipoles
sensitive to missing resonance states

8. Standard Analysis Approach
known resonance parameters
(mass, width, quantum numbers, hadronic couplings)
Analysis
photo- and electro-production data base
(mostly differential cross sections)
electromagnetic transition form factors

9. e p e X at 4 GeV
events
CLAS

10. CLAS Coverage for e p e’ X
5.0
4.0
3.0
2.0
For electron scattering experiments CLAS is usually triggered on electrons only.
The inclusive electron spectrum at 4 GeV beam energy,
shown here in the Q2 versus invariant mass W kinematics, exhibits the elastic scattering band, the 3 resonance bands, and the transition to the deep inelastic regime.
These lines indicate the region where many of the missing states are expected.
(next slide)
The projection onto the W axis shows the elastic peak and the
3 resonance bumps
1.0
CLAS
1.0
1.5
2.0
2.5

11. CLAS Coverage for e p e’ p X, E=4 GeV
2.0
missing states
1.5
pi0, eta, or omega in the
final state. The missing mass vs invariant mass scatter plot shows clear correlations of resonance excitations and specific final states.
Strong excitation near 1500 is correlated with the p-eta channel, and there is a lot of strenght in p-omega throughout the higher mass region.
The Delta sticks out in the p-pi0 channel, and can best be studied in this channel.
1.0
CLAS 0.
0.5
1.0
1.5

12. Resonance Contributions to g*p pw ?
CLAS
above resonance
region
cos qw +1 -1 s p g w N* in
resonance region

13. Resonances in Hyperon Production?
CLAS
g*p K+Y
forward hemisphere
backward hemisphere
preliminary
N* ?

14. Resonances in g*p pp+p-
CLAS
Analysis performed by Genova-Moscow collaboration
step #1:
use the best information presently available
GNpp from PDG
GNg AO/SQTM
These are the first high statistics electroproduction data in the 2-pi channel.
The data can be best fitted by a new P13 state with properties that are very different from the properties of the known
P13 located in the same mass range.
extra strength
W(GeV)

15. Attempts to fit observed extra strength
CLAS
Analysis step #2:
- vary parameters
of known D13
introduce new P13 or
alternate possibilities, e.g. an increase in D13(1700) strength give poorer fits especially to the hadronic distributions, ...
P13
D13(1700)
W(GeV)

16. Summary of g*p p p+ p- Analysis
CLAS data at variance with N* information in PDG
Describing data requires
major modifications of the parameters of known resonances, or
introduction of new P13 resonance with
M = / GeV
(consistent with “missing” P13 state, but mass lower than predicted)
GT = 88 +/- 17 MeV
D p : /- 0.13
N r : /- 0.10
Next steps:
more experimental data already in hand
combined analysis with other decay channels:
has been seen in hadronic analyses ...
A new P13 would be consistent with a "missing state" by Capstick & Roberts, except for a 130MeV lower mass....
(next slide, omega)
While many resonances are known to decay into the 2-pion channel not a single resonance listed in the RPP is known to couple to the N-omega channel. Therefore, any state seen in that channel would be a discovery, either of a new decay, or of a missing state.
(next) Why is the search for at least some of the missing states so important for the understanding of baryon structure? ...
p N
h N
K L

17. Electromagnetic Probe
helicity amplitudes very sensitive to the difference in wave functions of N and N*
can separate electric and magnetic parts of the transition amplitude
varying Q2 allows to change the spatial resolution and enhances different multipoles
sensitive to missing resonance states

18. N D(1232) Transition Form Factors
SU(6): E1+=S1+=0
The Delta excitation has been studied experimentally for 3 decades, and the dominant magnetic dipole transition is well established, mediated by a simple spin flip. Electric or scalar quadrupole transitions, which are identical 0 in a symmetry SU(6) model, would indicate a deformation of the Delta and the nucleon.
Dynamically, such contributions may arise through interaction with the pion cloud, or through the one gluon exchange.
helicity conservation requires that the E/M asymptotically approaches +1. Qualitatively one expects such a behavior. The sign of the this ratio is related to the shape of the deformation of the Delta
in such a way.

19. Multipoles E1+/M1+, S1+/M1+ (before 2001)
Hall C
This shows the data on the electric quadrupole of
magnetic dipole ratio and the scalar quadrupole to magnetic dipole ratio. The colored points are mostly from the
seventies and exhibit large systematic discrepancies.
The more recent data indicate that REM is small and negative,
-2% to -3%, and has a weak Q2 dependence, while RSM may
have a stronger Q2 dependence if one ignores this point.
Today, the emphasis is on control of systematics.
While in spectrometer experiments the kinematics needs to be adjusted many times during a measurement CLAS measures all kinematics simultaneously.
Hall C

20. Kinematics and Cross Sections
example:
e p e’ p po
Extracting the multipoles requires first to separate the relevant response function, by measureing the azimuthal and polar angle dependence of the diff. cross section, and fitting it to the expected phi dependence, (next slide)
as shown in this graph.....

21. CLAS
need broad coverage in pion decay angles cos(q*) and F
cos(q*) F

22. Multipole Analysis for g*p p po
CLAS
Q2 = 0.9 GeV2
|M1+|2
Re(E1+M1+*) |M1+|2
and with some approximation analysed in terms of multipoles.
The first terms is dominated by the transverse component
and strongly dependent on the dominant magnetic dipole transition, while the TT interference is most sensitive to the
electric quadrupole, and the LT interference to the scalar quadrupole.
(new graph)
Overlaying the new results on the old data....
Re(S1+M1+*)

23. Multipoles E1+/M1+, S1+/M1+ (2002)
Hall C
bridging the photon point for REM and the high Q2 results from earlier JLAB measurements. The REM ratio remains small and negative around -2% with little Q2 dependence.
The RSM ratio shows a strong Q2 dependence and becomes increasingly negative at higher Q2.
(next graph)
For comparison with some selected models I eliminate
old data and blow up the vertical scale....

24. Theoretical Interpretation of E1+/M1+, S1+/M1+
Bonn(2002)
Data are compared with two relatized CQMs, a chiral quark soliton model, and a dynamical model with hadronic degrees of freedom. Non of the pure quark models is successful in describing both ratios, simultaneously.
The comparison strengthens the claim that most of the quadrupole strength is due to non-resonant meson exchange, implemented in the dynamical models.
A dynamical model by Kamalov and Yang, using a different unitarization procedure, gives similiarly good agreement with the data.
One should note that these models have been fitted to the photon point and the high Q2 data.
(next slide)
Ultimately, we want to come to a QCD description of these quantities.
Currently there is only one calculation in quenched QCD
for REM with a large error bar....

25. N D Transition, what’s next?
systematic uncertainties in extraction of E1+/M1+ from ep e’p po around 0.5%
differences in treatment of background terms (models not constrained)
will become more severe for higher Q2 (D dropping faster)
more experimental information in hand (analysis in progress)
cross sections e p e’p (po) Q2 = (1.5 – 5.5) GeV2
single-spin asymmetry sTL’ for e p e’p (po) and e p e’ p+ (n)
polarization transfer in e p e’ p (po)
differential cross sections for e p e’ p+ n (D less important)
experiments in the near future
extend Q2 range to 0.05 GeV2 (end of 2002)
extend Q2 range to ~7 GeV2 (1st half of 2003)
CLAS
CLAS
Hall A
CLAS
CLAS
Hall C

26. Polarized Beam Observables
CLAS
sLT’ response
function for
e p e p po
sLT’ = 0 if only a single diagram contributes (sensitive to the interference between D and background)
The Mami beam asymmetry data at large cms angles show a strong sensitivity to model descriptions is. The dotted line is a rescaled MAID model.
The CLAS data on the sigma_LT' response function cover the full angle range and show similar sensitivity to model descriptions.
Since the resonance contributions are nearly the same in either model, the discrepancies are largely due to the different description of non-resonant terms.

27. Polarization Measurement in e p e’ p (po)
Hall A
Q2 = 1 GeV2
W = GeV
Results sensitive to non-resonant contributions
Parametrisations of available data
SAID MAID

28. p+ Electroproduction CLAS
allows ectraction of resonant amplitudes in the 2nd resonance region.
(next slide)
the next graph shows the preliminary results for one Q2 point on the Roper resonance....

29. Summary
Understanding the structure of bound qqq systems is a central problem for the study of QCD in the strong coupling regime
Specific issue #1: identify relevant degrees-of-freedom
finally getting electromagnetic data of sufficient quality to study missing resonance problem
initial data strongly suggest resonance contributions that cannot be explained by known baryon states
Specific issue #2: probing details of quark wave functions
consistent data set for N D transition up to Q2 = 4 GeV2
E1+/M1+ small and negative
data emphasize the importance of pion degrees-of-freedom and relativity